Marie distributes toys for toddlers. She makes visits to households and gives away one toy only on visits for which the door is answered and a toddler is in residence. On any visit, the probability of the door being answered is 3/4, and the probability that there is a toddler in residence is 1/3. Assume that the events “Door answered" and “Toddler in residence" are independent and also that events related to different households are independent.
1)What is the probability that she has not distributed any toys by the end of her second visit?
2)What is the probability that she gives away the first toy on her fourth visit?
3) We will say that Marie “needs a new supply"" immediately after the visit on which she gives away her last toy. If she starts out with three toys, what is the probability that she completes at least five visits before she needs a new supply?
4) If she starts out with exactly six toys, what is the expected value of the number of houses with toddlers that Marie visits without leaving any toys (because the door was not answered) before she needs a new supply?
1. 9/16
2. 27/256
3. 9/64
4. 27/256
5. 1/8
6. 243/256
7. 2
three visits none, then one?
first none on three visits
= 3/4 * 3/4 *3/4 = 27/64 then strike gold (27/64)(1/4)
that is 2.
pd = (3/4) = p door ans
pc = (1/3) = p child there
pdc = (3/4)(1/3) = probability door ans and child there = pt = p toy at that door = (1/4)
1 - (1/4) = (3/4) = prob no toy given at that door
twice in a row and independent?
(3/4)(3/4) = 9/16
That is question 1.
Now you try.
Thanks for first 2 i tried 3 and 4 but i got
3 ) 0.14
4)
0.1667
but both are wrong ...
could you help
This is Problem description
--------------------------------------
Marie distributes toys for toddlers. She makes visits to households and gives away one toy only on visits for which the door is answered and a toddler is in residence. On any visit, the probability of the door being answered is 3/4, and the probability that there is a toddler in residence is 1/3. Assume that the events “Door answered" and “Toddler in residence" are independent and also that events related to different households are independent.
and i'm trying to find out the probability for these 4 cases
1)What is the probability that she has not distributed any toys by the end of her second visit?
2)What is the probability that she gives away the first toy on her fourth visit?
3) We will say that Marie “needs a new supply"" immediately after the visit on which she gives away her last toy. If she starts out with three toys, what is the probability that she completes at least five visits before she needs a new supply?
4) If she starts out with exactly six toys, what is the expected value of the number of houses with toddlers that Marie visits without leaving any toys (because the door was not answered) before she needs a new supply?
Thanks